1) \( \frac{x}{2}+3>9 \)

To solve the inequality \( \frac{x}{2}+3>9 \), start by isolating \( x \). Subtract 3 from both sides to get \( \frac{x}{2} > 6 \). Next, multiply both sides by 2, leading to \( x > 12 \). So, any value greater than 12 will satisfy this inequality! Now, if you want to test your solution, plug in a number greater than 12, like 13. You'll see that \( \frac{13}{2}+3 \) equals 6.5 + 3 = 9.5, which is greater than 9. This is a solid confirmation that you’re on the right track!